In this paper, we propose a smoothing sequential quadratic programming (SSQP) algorithm for solving a class of nonsmooth nonconvex, perhaps even non-Lipschitz minimization problems, which has wide applications in statistics and sparse reconstruction. At each step, the SSQP algorithm solves a strongly convex quadratic minimization problem with a diagonal Hessian matrix, which has a simple … Read more
We discuss a bundle method to minimize non-smooth and non-convex locally Lipschitz functions. We analyze situations where only inexact subgradients or function values are available. For suitable classes of non-smooth functions we prove convergence of our algorithm to approximate critical points. CitationTo appear in: Computational and Analytical Mathematics. Springer Proceedings in MathematicsArticleDownload View PDF
Facility location-network design problems seek to simultaneously determine the locations of fa- cilities and the design of the network connecting the facilities so as to best serve a set of clients accessing the facilities via the network. Here we study a dynamic (multi-period) version of the problem, subject to a budget constraint limiting the investment … Read more
Model Predictive Control (also known as Receding Horizon Control (RHC)) has been highly successful in process control applications. Its use for aerospace applications has been hindered by its high computational requirements. In the present paper, we propose using enhanced primal-dual interior-point optimization techniques in the convex-quadratic-program-based RHC control of a rotorcraft. Our enhancements include a … Read more
In this paper, we propose a primal IP method for solving the optimal experimental design problem with a large class of smooth convex optimality criteria, including A-, D- and p th mean criterion, and establish its global convergence. We also show that the Newton direction can be computed efficiently when the size of the moment … Read more
The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, while minimizing the weighted sum of the distances between all pairs of facilities. The problem is NP-hard. In this paper, we present two tabu search implementations, one involving an exhaustive search of the 2-opt neighborhood and … Read more
The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, while minimizing the weighted sum of the distances between all pairs of facilities. The problem is known to be NP-hard. In this paper, we present a neighborhood search heuristic called LK-INSERT which uses a Lin-Kernighan neighborhood … Read more
The contributions of the first half of this thesis are on the computational and algebraic aspects of convexity in polynomial optimization. We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves … Read more
Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy data sets. Over the years, a variety of heuristics have been proposed to solve this complex optimisation problem, with good results in some cases yet with limitations in … Read more
In this paper we consider robust models of surge capacity plans to be deployed in the event of a flu pandemic. In particular, we focus on managing critical staff levels at organizations that must remain operational during such an event. We develop efficient procedures for managing emergency resources so as to minimize the impact of … Read more